## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Module MAT-40-17-M-7

## Module Identification

Module Number Module Name CP (Effort)
MAT-40-17-M-7 Group Theory 9.0 CP (270 h)

## Basedata

CP, Effort 9.0 CP = 270 h 1 Sem. irreg. [7] Master (Advanced) [EN] English Malle, Gunter, Prof. Dr. (PROF | DEPT: MAT) Fieker, Claus, Prof. Dr. (PROF | DEPT: MAT) Lassueur, Caroline, Jun. Prof. Dr. (PROF | DEPT: MAT) Malle, Gunter, Prof. Dr. (PROF | DEPT: MAT) Thiel, Ulrich, Prof. Dr. (PROF | DEPT: MAT) [MAT-AGCA] Algebra, Geometry and Computer Algebra [MAT-88.105-SG] M.Sc. Mathematics [NORM] Active

## Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V MAT-40-17-K-7
Group Theory
P 56 h 214 h - - PL1 9.0 irreg.
• About [MAT-40-17-K-7]: Title: "Group Theory"; Presence-Time: 56 h; Self-Study: 214 h

## Examination achievement PL1

• Form of examination: oral examination (20-30 Min.)
• Examination Frequency: each semester
• Examination number: 84170 ("Group Theory")

## Contents

• Abelian groups, solvable and nilpotent groups,
• permutation groups and linear groups,
• Mathieu groups,
• Frattini and Fitting groups,
• extensions of groups,
• free groups and presentations.

## Competencies / intended learning achievements

Upon successful completion of the module, the students know and understand the basic principles and methods of the theory of finite groups. They have studied important examples of finite groups and are able to examine those using scientific methods. They are able to name the main propositions of the lecture, classify and explain the illustrated relationships. They understand the proofs and are able to reproduce and explain them. In particular, they can critically assess, what conditions are necessary for the validity of the statements.

By completing exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and methods taught in the lecture.

## Literature

• B. Huppert: Endliche Gruppen I,
• H. Kurzweil: Endliche Gruppen,
• D. Gorenstein: Finite Groups.

None

## References to Module / Module Number [MAT-40-17-M-7]

Module-Pool Name
[MAT-43-MPOOL-7] Specialisation Algebra and Number Theory (M.Sc.)
[MAT-RM-MPOOL-7] Pure Mathematics (Advanced Modules M.Sc.)